Page 359 - Introduction to Statistical Pattern Recognition

7 Nonparametric Classification and Error Estimation 34 1

TABLE 7-3

EFFECT OF ESTIMATED COVARIANCE MATRICES
FOR THE PARZEN APPROACH

Data Bayes Covariance Leave-one-out cr~ Resubstitution OR
Error(%) Used Error(%) (%) Error(%) (%)
1-1 10 True 11.0 I .8 6.4 1.3
Estimated 12.6 2.6 5.8 1.3
1-41 9 True 10.6 2.9 4.8 1 .o
Estimated 11.0 3.2 4.5 1.3
I-A 1.9 True 2.0 1.2 1.1 0.9
Estimated 2.3 0.9 0.8 0.6

(a) Standard data sets

Case Cov. Nco,, N Leave-one-out Resubstitution
- used (%I (%)
1 5; 8800 720 17.8 16.2
8800 360 19.5 15.6

2 &(L) 720 720 23.3 7.1
,. 360 360 27.4 3.8
3 E, 720 720 8.4 7.1
360 360 5.2 3.8

(b) Data RADAR

used shows that the estimated covariance always gives a larger upper bound
and smaller lower bound than the true covariance, although the differences are
small. The standard deviations of 10 trials, 0, and o,, are also presented in
Table 7-3.